Algebra 1 Graphing Functions

When it comes to graphing functions, we use a lot of the tools that we use with graphing just a normal equation. We will see first how you can use a chart to plot a whole bunch of different points and graph out an entire function. However, if you have a linear function, we can often use our tools for lines to shortcut that process. Once we can look at the graph of the function, we will be able to determine whether it is truly a function using the vertical line test. More importantly, once we have the graph of the function we can test out what its domain and range is just from looking at its graph.

Graphing Functions

We can graph functions using a table of values. This is the same process that is used for graphing equations.

To create a table of values, choose several values for the independent variable, then evaluate the function for these values. This will develop of a list of ordered pairs (inputs, outputs) that can be plotted.

You can determine if a graph is a function by using the vertical line test. If the graph crosses a vertical line in more than one spot, it is not a function.

To determine the domain and range of a function from its graph, trace points back to the x-axis and y-axis. The points traced back to the x-axis will cover the domain. The points traced back to the y-axis will cover the range.

Graphing Functions

A line passes through the points (5,4) and (0,8). Find the equation of the line in slope intercept form.

y = mx + bslope = [(y2 − y1)/(x2 − x1)]

slope = [(8 − 4)/(0 − 5)] = [4/( − 5)]

y = − [4/5]x + 8

A line passes through the points ( - 3,6) and (0, - 6). Find the equation of the line in slope intercept form.

y = mx + bslope = [(y2 − y1)/(x2 − x1)]

slope = [( − 6 − 6)/(0 − ( − 3))]

slope = [( − 12)/3]

slope = − 4

y = − 4x − 6

A line has slope - 4 and passes through ( - 10, - 8). Find its equation in slope intercept form.

y = mx + b

m = − 4b = ?

− 8 = − 4( − 10) + b

− 8 = 40 + b

b = − 48

y = − 4x − 48

A line has slope - 1 and passes through (7,15). Find its equation in slope intercept form.

y = mx + b

m = − 1b = ?

15 = − 1(7) + b

15 = − 7 + b

22 = b

y = − 1x + 22

y = − x + 22

A line passes through the points (4,1) and (0,6). Find the equation of the line in slope intercept form.

slope = m = [(y2 − y1)/(x2 − x1)]

m = [(6 − 1)/(0 − 4)]

m = [5/( − 4)]

y = mx + b

y = − [5/4]x + 6

A line has slope - 7 and passes through ( - 8,11). Find its equation in slope intercept form.

y = mx + b

m = − 7 b = ?

11 = − 7( − 8) + b

11 = 56 + b

− 45 = b

y = − 7x − 45

A line passes through the points ( - 2, - 3) and (4, - 2). Find the equation of this line in slope intercept form.

m = [(y2 − y1)/(x2 − x1)]

m = [( − 2 − ( − 3))/(4 − ( − 2))]

m = [1/6]

y = mx + b

− 3 = [1/6]( − 2) + b

− 3 = − [2/6] + b

− 2[4/6] = b

y = [1/6]x − 2[4/6]

A line passes through the points (5, - 4) and ( - 1,6). Find the equation of this line in slope intercept form.

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Graphing Functions

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